Bolzano–Weierstrass theorem
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states that each bounded sequence in Rn has a convergent subsequence. An equivalent formulation is that a subset of Rn is sequentially compact if and only if it is closed and bounded. The theorem is sometimes called the sequential compactness theorem.
known for
notableIdea
Wikipage disambiguates
Bolzano-WeierstrassBolzano-Weierstrass TheoremBolzano-Weierstrass Theorem.Bolzano-Weierstrass propertyBolzano-Weierstrass theoremBolzano-WeierstraßBolzano-Weierstraß theoremBolzano-weierstraßBolzano theoremBolzano weierstrassBolzano–Weierstraß theoremSequential compactness theoremTheorem of Bolzano-Weierstrass
Wikipage redirect
Arzelà–Ascoli theoremBernard BolzanoBolzano-WeierstrassBolzano-Weierstrass TheoremBolzano-Weierstrass Theorem.Bolzano-Weierstrass propertyBolzano-Weierstrass theoremBolzano-WeierstraßBolzano-Weierstraß theoremBolzano-weierstraßBolzano theoremBolzano weierstrassBolzano–Weierstraß theoremCauchy sequenceCompact spaceCompleteness of the real numbersEkeland's variational principleExtreme value theoremGeometric meanGeometric–harmonic meanHeine–Borel theoremHilbert spaceIvar EkelandKakutani fixed-point theoremKarl WeierstrassLeast-upper-bound propertyList of mathematical proofsList of real analysis topicsList of theoremsList of things named after Karl WeierstrassNet (mathematics)Ralph P. Boas Jr.Real analysisReal coordinate spaceReverse Mathematics: Proofs from the Inside OutReverse mathematicsSecond-order arithmeticSequential compactness theoremSubsequenceTheorem of Bolzano-Weierstrass
Link from a Wikipage to another Wikipage
known for
notable ideas
primaryTopic
Bolzano–Weierstrass theorem
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states that each bounded sequence in Rn has a convergent subsequence. An equivalent formulation is that a subset of Rn is sequentially compact if and only if it is closed and bounded. The theorem is sometimes called the sequential compactness theorem.
has abstract
Bolzano-Weierstrass sats är en ...... i har en konvergent delföljd.
@sv
Der Satz von Bolzano-Weierstra ...... stenz konvergenter Teilfolgen.
@de
En anàlisi real, el teorema de ...... amb el teorema de Heine-Borel.
@ca
En el análisis real, el teorem ...... tos compactos secuencialmente.
@es
En topologie des espaces métri ...... d Bolzano et Karl Weierstrass.
@fr
Il teorema di Bolzano-Weierstr ...... nome di entrambi gli studiosi.
@it
In de wiskundige analyse, een ...... s dan als deze gesloten en is.
@nl
In mathematics, specifically i ...... equential compactness theorem.
@en
O teorema de Bolzano-Weierstra ...... alguma esfera de raio finito.
@pt
Twierdzenie Bolzana-Weierstras ...... matematyka Karla Weierstrassa.
@pl
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,022,737,613
Link from a Wikipage to another Wikipage
id
p/b016880
@en
title
Bolzano-Weierstrass theorem
@en
wikiPageUsesTemplate
hypernym
comment
Bolzano-Weierstrass sats är en ...... i har en konvergent delföljd.
@sv
Der Satz von Bolzano-Weierstra ...... stenz konvergenter Teilfolgen.
@de
En anàlisi real, el teorema de ...... amb el teorema de Heine-Borel.
@ca
En el análisis real, el teorem ...... tos compactos secuencialmente.
@es
En topologie des espaces métri ...... d Bolzano et Karl Weierstrass.
@fr
Il teorema di Bolzano-Weierstr ...... po la dimostrazione del primo.
@it
In de wiskundige analyse, een ...... s dan als deze gesloten en is.
@nl
In mathematics, specifically i ...... equential compactness theorem.
@en
O teorema de Bolzano-Weierstra ...... alguma esfera de raio finito.
@pt
Twierdzenie Bolzana-Weierstras ...... przestrzeniach metryzowalnych.
@pl
label
Bolzano–Weierstrass sats
@sv
Bolzano–Weierstrass theorem
@en
Satz von Bolzano-Weierstraß
@de
Stelling van Bolzano-Weierstrass
@nl
Teorema de Bolzano-Weierstrass
@ca
Teorema de Bolzano-Weierstrass
@es
Teorema de Bolzano-Weierstrass
@pt
Teorema di Bolzano-Weierstrass
@it
Théorème de Bolzano-Weierstrass
@fr
Twierdzenie Bolzana-Weierstrassa
@pl